Random permutations and unique fully supported ergodicity for the Euler adic transformation

Abstract

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.Comment: 12 pages, 7 figures, to appear Ann. Inst. H. Poincar\'e Prob. and Sta